A wave travelling along a string is described by, `y(x, t) = 0.005 "sin" (80.0 x – 3.0 t)`, in which the numerical constants are in SI units `(0.005 m, 80.0 "rad" m^(-1)`, and `3.0 "rad" s^(-1))`. Calculate (a) the amplitude, (b) the wavelength, and (c) the period and frequency of the wave. Also, calculate the displacement y of the wave at a distance x = 30.0 cm and time t = 20 s ?

Answer

A, B, C, D

Explanation

On comparing the given equation with
`y(x,t)`= `A sin (kx-omegat)`, we find
(a) the amplitude `A =0.005m= 5 mm`.
(b) the angular wave number k and angular frequency omega are
` k=80.0 m^-1` and `omega= 3.0 s^-1`
`:. lambda=2pi//k =(2pi)/(80.0)=0.0785m`
7.85cm
(c) `T=2pi//omega=(2pi)/(3.0)=2.09s`
and frequency, `f=1//T =0.48Hz`
The displacement y at `x =30.0cm` and time `t =20s` is given by
`y=(0.005m)sin (80.0xx0.3 -3.0xx20)`
`=(0.005m) sin(-36)`
`=(0.005m)sin (-36+12pi)`
`=(0.005m)sin (1.714)`
`=(0.005m)sin(98.27^@)=4.94mm`